Three mathematicians are applying for a job. there are five hats, three white, two black. they’re lined up, and a hat is placed on each. the first person in line cannot see any hat; the second in line sees only the hat of the person in front of him; the third person sees only the hats of the two people in front of her. the first person to correctly figure out what color hat he has gets the job; you guess wrong and you are killed. assume these are intelligent mathematicians, and that they will do the logically correct thing at each stage — if something can be deduced, they will figure it out.
after a long pause, the first person, who cannot see any hats, says he knows the color of his hat. what is the color, and how does he know?